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Simplifying (9x + -9)(10x + 5) = 0 Reorder the terms: (-9 + 9x)(10x + 5) = 0 Reorder the terms: (-9 + 9x)(5 + 10x) = 0 Multiply (-9 + 9x) * (5 + 10x) (-9(5 + 10x) + 9x * (5 + 10x)) = 0 ((5 * -9 + 10x * -9) + 9x * (5 + 10x)) = 0 ((-45 + -90x) + 9x * (5 + 10x)) = 0 (-45 + -90x + (5 * 9x + 10x * 9x)) = 0 (-45 + -90x + (45x + 90x2)) = 0 Combine like terms: -90x + 45x = -45x (-45 + -45x + 90x2) = 0 Solving -45 + -45x + 90x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '45'. 45(-1 + -1x + 2x2) = 0 Factor a trinomial. 45((-1 + -2x)(1 + -1x)) = 0 Ignore the factor 45.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-0.5, 1}
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